Global Existence for Reaction-Diffusion Systems on Multiple Domains

Global existence for semilinear reaction-diffusion systems on evolving domains.

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that comm...

On the Existence and Nonexistence of Global Solutions of Reaction-diffusion Equations in Sectorial Domains

In this paper we study the first initial-boundary value problem for u, = Au + up in conical domains D = (0,oo) x Í2 c RN where Í2 C SN~l is an open connected manifold with boundary. We obtain some extensions of some old results of Fujita, who considered the case D = RN . Let X = — ywhere y_ is the negative root of y(y + N 2) = wx and where wx is the smallest Dirichlet eigenvalue of the Laplace-...

Global Existence of Solution for Reaction Diffusion Systems with a Full Matrix of Diffusion Coefficients

The goal of this work is to study the global existence in time of solutions for somecoupled systems of reaction diffusion which describe the spread within a population of infectiousdisease. We consider a full matrix of diffusion coefficients and we show the global existence of thesolutions.Full text References[1] N. D. Alikakos, L-Bounds of Solutions of Reaction-Diffusion Eq...

On Existence and Nonexistence Global Solutions of Reaction-Diffusion Equations

We consider the initial value problem for the reaction-diffusion equation ut = ∆u + f(u). In this paper we show the existence and nonexistence of the global solutions in time. Especially, we extend the condition of the nonlinear terms to more general. We have the results of the existence and the nonexistence for the equation with the nonlinear term f satisfying lim infs→0 f(s)/sp > 0 and lim su...

Global existence and fast-reaction limit in reaction-diffusion systems with cross effects